A cube is cut with 3 straight cuts. If these cuts can be either horizontal or vertical, what is the percentage increase in toatal surface area
Answers
Given :- A cube is cut with 3 straight cuts . Either horizontally or vertically . What is the percent increased in the total surface area of the cube ?
Answer :-
Let us assume that, the cube has a side of 3x unit .
so,
→ TSA of initial cube before cut = 6(side)² = 6(3x)² = 54x² .
now, when cubes is cut with 3 straight cuts, lets say it cuts with horizontally, then, one side will cut into 3 parts of x cm each and rest will be same . similarly, if cuts vertically .
conclusion :-
- we gets three cuboid of side as x unit, 3x unit and 3x unit .
then,
→ TSA of resulting 3 cuboid so formed = 3*2[lb + bh + hl] = 6[x*3x + 3x*3x + 3x*x] = 6 * 15x² = 90x²
therefore,
→ Increased TSA = 90x² - 54x² = 36x² .
hence,
→ % increased in TSA = (36x² * 100) / 54x² = 66.67% (Ans.)
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